We have to find value of the integral
I = ∫cos2θ+16sin2θdθ
Using the substitution,
sin2θ=2cosθsinθ
= ∫−cos2θ+16−12sinθcosθdθ
Substitute u=cos2θ+16
dθdu=−2cosθsinθ
Hence,
dθ=−2cosθsinθdu
Hence integral will become
−∫udu
=−2u
Using substitution u=cos2θ+16
We get , I=−2cos2θ+16+C
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